1. Field of the Invention
The present invention relates to signal decomposition and reconstruction in sub-band coding and, more particularly, to analysis and synthesis filter banks that are designed according to the Quadrature Mirror Filter concept such that the sub-band coding of various types of signals may be accomplished with minimal computational complexity so as to result in perfect signal reconstruction.
2. Description of the Prior Art
Sub-band coding refers to a technique wherein, by the parallel application of a set of filters, an input signal is decomposed into a number of narrow band signals that are separately decimated and coded for the purpose of transmission. After transmission the signals are decoded, interpolated, and filtered so as to reconstruct the original signal. Originally, sub-band coding was developed for the transmission of speech signals (see e g. R. E. Crochiere et al., "Digital Coding of Speech in Sub-bands", BSTJ Vol. 55, pp. 1069-1085). More recently, however, sub-band coding has been used for the transmission of video signals (see e.g. J. W. Woods et al., "Subband Coding of Images" IEEE Transactions on Acoustics, Speech, and Signal Processing, Vol. ASSP-34, pp. 1278-1288, October 1986).
When designing a sub-band coding scheme, great emphasis is placed on the selection of analysis and synthesis filter banks. Such analysis and synthesis filter banks are used to decompose and reconstruct, respectively, the original signal. Much of the design work for these filter banks has been motivated by speech signal processing, wherein sharp band separation is a very desirable property. This work has led naturally to finite impulse response (FIR) filter banks with a large number of stages, e.g. 64. A classical approach to designing such filter banks is the Quadrature Mirror Filter approach, which allows substantially exact reconstruction of input speech signals (see e.g. D. Esteban et al., "Application of Quadrature Mirror Filters to Split Band Voice Coding Schemes", Proceedings of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP), pp. 191-195, 1977). Application of the Quadrature Mirror Filter concept to the sub-band coding of video signals has recently received considerable attention since it has been shown that this approach is highly effective for image compression (see e.g. M. Vetterli, "Multi-dimensional Sub-band Coding: Some Theory and Algorithms", Signal Processing (1984), pp. 97-112; H. Gharavi et al., "Sub-band Coding of Digital Images Using Two-Dimensional Quadrature Mirror Filter" Proc SPIE, Vol 707, pp 51-61, September 1986; J. W. Woods et al., "Sub-Band Coding of Images" Proc ICASSP, pp 1005-1008, April 1986; H. Gharavi et al., "Application of Quadrature Mirror Filtering to the Coding of Monochrome and Color Images", Proc. ICASSP, Vol. 4, pp. 2384-2387, 1987; P. H. Westerink et al., "Sub-Band Coding of Digital Images Using Predictive Vector Quantization" Proc ICASSP, Vol 3, pp. 1378-1381, 1987). To date, however, substantially exact reconstruction of video signals using the Quadrature Mirror Filter concept has only been achieved through the use of long, multiple stage filter banks which are complex in hardware implementation and are computationally intensive.
A variety of other filter bank designs have been proposed which allow exact, or perfect, reconstruction of various types of sub-band coded signals (see e.g. M. Smith et al., "Exact Reconstruction Techniques for Tree Structured Subband Codes" IEEE Transactions on ASSP, Vol ASSP-34, pp 434-441, June 1986; M. Vetterli, "Filter Bands Allowing Perfect Reconstruction" Signal Processing, Vol. 10, No. 3, pp. 219-244, April 1986). However, these filter bank designs have not proven entirely satisfactory for the perfect reconstruction of sub-band coded video signals because of their high computational complexity. More recently, however, filter banks have been designed which allow for the perfect reconstruction sub-band coded video signals, wherein the individual filters in the analysis and synthesis filter banks are designed to be linear in phase, symmetrical in time, and to have unequal bandwidth frequency responses (see U.S. Pat. No. 4,829,378 by LeGall). Although these non-QMF filter banks are relatively easy to implement in hardware and allow for the perfect reconstruction of sub-band coded video signals with a relatively small amount of computational complexity, the unequal bandwidth frequency responses result in the original signal being disproportionately filtered, decimated, and coded during the decomposition stage, and disproportionately decoded, interpolated, and filtered during the reconstruction stage. As a consequence of the disproportionate filtering, such filter banks exhibit deteriorating frequency responses when used in hierarchical sub-band structures.
Although all of the above-mentioned filter bank designs allow for the sub-band coding of various types of signals, none employ the Quadrature Mirror Filter concept in the design of analysis and synthesis filter banks to the point where hardware implementation is easily obtained and sub-band coding of signals is accomplished with minimal computational complexity so as to result in perfect signal reconstruction. Such analysis and synthesis Quadrature Mirror Filter banks would be desirable since, as previously described, the Quadrature Mirror Filter approach has been shown to be highly effective for signal analysis, synthesis and generation. It would therefore be desirable to provide such analysis and synthesis Quadrature Mirror Filter banks so as to overcome the practical shortcomings of the prior art filter bank designs.